The logarithmic Cauchy quotient mean
Martin Himmel, Janusz Matkowski
TL;DR
This paper introduces a new family of means based on logarithmic Cauchy quotient functions, motivated by recent developments in beta-type functions, and provides their characterization.
Contribution
It defines and characterizes a novel family of means of logarithmic Cauchy quotient type, expanding the theory of mathematical means.
Findings
New family of means introduced and characterized
Connections to beta-type functions established
Potential applications in mathematical analysis suggested
Abstract
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical Inequalities and Applications · Approximation Theory and Sequence Spaces